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 A274068 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..2 order. 3

%I #4 Jun 09 2016 08:08:52

%S 1,2,2,5,9,5,14,50,50,14,41,285,136,285,41,122,1129,111,111,1129,122,

%T 365,4791,97,0,97,4791,365,1094,17219,235,0,0,235,17219,1094,3281,

%U 63640,197,0,0,0,197,63640,3281,9842,182143,389,0,0,0,0,389,182143,9842,29525

%N T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..2 order.

%C Table starts

%C ......1........2...5..14...41..122...365..1094...3281...9842...29525...88574

%C ......2........9..50.285.1129.4791.17219.63640.182143.598332.1622713.4807733

%C ......5.......50.136.111...97..235...197...389....305....589.....447.....823

%C .....14......285.111...0....0....0.....0.....0......0......0.......0

%C .....41.....1129..97...0....0....0.....0.....0......0......0

%C ....122.....4791.235...0....0....0.....0.....0......0

%C ....365....17219.197...0....0....0.....0.....0

%C ...1094....63640.389...0....0....0.....0

%C ...3281...182143.305...0....0....0

%C ...9842...598332.589...0....0

%C ..29525..1622713.447...0

%C ..88574..4807733.823

%C .265721.12097755

%C .797162

%H R. H. Hardin, <a href="/A274068/b274068.txt">Table of n, a(n) for n = 1..108</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2)

%F k=3: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5) for n>13

%e Some solutions for n=3 k=4

%e ..0..1..1..0. .0..0..1..1. .0..1..2..1. .0..1..1..0. .0..0..0..1

%e ..2..2..2..0. .2..1..2..0. .0..1..2..1. .2..2..2..2. .2..2..1..0

%e ..1..1..0..2. .2..1..2..0. .2..0..0..2. .1..1..0..0. .1..1..2..0

%Y Column 1 is A007051(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 09 2016

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Last modified August 14 16:54 EDT 2024. Contains 375166 sequences. (Running on oeis4.)